What is Outcomes and events?

Also known as: random experiment · sample space · event

Definition 9.1 High School Mathematics · Chapter 9 — Probability and Sampling

A random experiment is an experiment whose result cannot be predicted (rolling a die). The set of all possible results is the sample space $\Omega = \{\omega_1, \dots, \omega_n\}$ ; its elements are the outcomes. An event is a set of outcomes; an event occurs when the result of the experiment belongs to it.

Examples

Example 9.4

Roll a fair die: $\Omega = \{1, 2, 3, 4, 5, 6\}$ , each outcome having probability $\frac16$ . The event $A$ : “the result is even” is $A = \{2, 4, 6\}$ , so $\P(A) = \frac36 = \frac12$ . The event $B$ : “the result is at least $5$ ” is $B = \{5, 6\}$ , so $\P(B) = \frac26 = \frac13$ .

Read in context →